Gainesville, FL 32611
George Michailidis, Ph.D.
Director of the Informatics Institute
Professor of Statistics and Computer Science
Title: Fast Randomized Algorithms for Tensor Operations and their Applications
Abstract: We consider scalable randomized algorithms for many common tensor operations, including low-rank approximation and decomposition, together with tensor multiplication. Such operations arise in a number of modern day applications of tensors in image and signal processing. Specifically, we introduce polynomial time algorithms that employ a small number of lateral and/or horizontal slices of the underlying 3-rd order tensor, that offer relative error guarantees for the quality of the solutions. All results can easily be extended to higher order tensors. We demonstrate the applicability of these algorithms on
diverse applications. The first focuses on mass spectrometry based imaging, where we use empirical statistical leverage scores of the input data to provide provably good low-rank
approximations of the measurements in the data that are expressed in terms of actual ions and positions, as opposed to the results obtained from difficult-to-interpret matrix decomposition techniques. Another illustration relates to image and video recovery, through a nuclear norm minimization approach, from incomplete and noisy data is
provided. Compared to existing state-of-the-art techniques, the proposed algorithms exhibit superior performance in both speed and solution quality.
Department of Industrial and Systems Engineering at the University of Florida